From the Mass Effect Wiki - Priority: Rannoch
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The other key is that the Reaper's aim is based on what you are doing when it starts firing, so if you make sure you're standing still until the beam appears, it won't "lead" you as much.
Note that on Casual, you don't have to do this twice. As soon as the beam touches ground, sprint to the side, turn, and fire. The Reaper will finish the attack, recharge, and try again. It won't make it. By the time the beam reaches you, you'll finish targeting and it will be hit from orbit. You only have to move once for every beam.
On insanity, it feels like the beam is faster, and being even close to the beam insta-kills you. As a result, you'll need to make wider sprints, corner to corner, giving you less time to fire. Same strategy applies, keep running, stand still, fire for eye. Except run further, corner to corner. As soon as Reaper starts firing, sprint, turn, fire. Tip: Performing a dive-roll as the last part of your sprints will help you get turned toward the reaper more quickly. Also, the beam only moves toward you, and does not double back. You can therefore sprint to the side and head toward the Reaper. Once the beam is behind you, you are safe.
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Think I ended up adjusting my settings to casual last time I did this battle and then turning the settings up after.